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cudgel (one's) brains
To try very hard to comprehend, solve, think of, or remember something. I was up all night cudgeling my brains for a way to pay off all my debts. She cudgeled her brains to remember the man's name.
take up the cudgels (for/on behalf of someone or something)
To defend, show strong support for, or argue on behalf of someone or something. People from across the country are taking up cudgels on behalf of the young man being held by police. He's got plenty of money to hire a proper legal team. I don't think he needs the likes of us taking up the cudgels.
take up (the) cudgels against (someone or something)
To prepare for or engage in a physical or verbal conflict against someone or something. People from across the country are taking up the cudgels against the dictatorship. We have to be willing to take up the cudgels if we ever want to loosen the grip of these greedy corporations.
take up arms (against someone or something)
to prepare to fight against someone or something. Everyone in the town took up arms against the enemy. They were all so angry that the leader convinced them to take up arms.
rack one's brain
Also, cudgel one's brains. Strain to remember or find a solution, as in I've been racking my brain trying to recall where we put the key, or He's been cudgeling his brains all day over this problem. The first term, first recorded in 1583 as rack one's wit, alludes to the rack that is an instrument of torture, on which the victim's body was stretched until the joints were broken. The variant, from the same period, uses cudgel in the sense of "beat with a cudgel" (a short thick stick). Shakespeare used it in Hamlet (5:1): "Cudgel thy brains no more about it, for your dull ass will not bend his pace with beating." Also see beat one's brains out.
take up arms
Also, take up the cudgels. Become involved in a conflict, either physical or verbal, as in The Kurds took up arms against the Iranians at least two centuries ago, or Some believe it's the vice-president's job to take up the cudgels for the president. The first term originated in the 1400s in the sense of going to war. The variant, alluding to cudgels as weapons, has been used figuratively since the mid-1600s and is probably obsolescent.
take up the cudgelsor
take up the cudgel
If you take up the cudgels for someone or take up the cudgel for them, you speak or fight in support of them. The trade unions took up the cudgels for the 367 staff who were made redundant. We are hoping that the government will take up the cudgel on our behalf. Note: A cudgel was a short, thick stick that was used as a weapon in the past.
cudgel your brain (or brains)think hard about a problem.
This expression was used by Shakespeare in Hamlet: ‘Cudgel thy brains no more about it’.
take up the cudgelsstart to support someone or something strongly.
take up the ˈcudgels for somebody/something,
take up the cudgels on behalf of somebody/something(old-fashioned, written) start to defend or support somebody/something: The local newspapers have taken up the cudgels on behalf of the woman who was unfairly dismissed from her job because she was pregnant.
A cudgel is a short thick stick that is used as a weapon.
take up the cudgels
To join in a dispute, especially in defense of a participant.